相关论文: Martingales, Detrending Data, and the Efficient Ma…

This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on…

We introduce a novel framework to account for sensitivity to rewards uncertainty in sequential decision-making problems. While risk-sensitive formulations for Markov decision processes studied so far focus on the distribution of the…

Given a set-valued stochastic process $(V_t)_{t=0}^T$, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors $\xi_t\in V_t$, admitting an equivalent martingale measure. The aim of this…

When expanding a filtration with a stochastic process it is easily possible for semimartingale no longer to remain semimartingales in the enlarged filtration. Y. Kchia and P. Protter indicated a way to avoid this pitfall in 2015, but they…

The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A class of regression models where cointegration works was…

In econometrics, the Efficient Market Hypothesis posits that asset prices reflect all available information in the market. Several empirical investigations show that market efficiency drops when it undergoes extreme events. Many models for…

We propose martingale consumption as a natural, desirable consumption pattern for any given (proportional) investment strategy. The idea is to always adjust current consumption so as to achieve level expected future consumption under the…

We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate…

This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…

We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal…

We study discrete-time stochastic processes $(X_t)$ on $[0,\infty)$ with asymptotically zero mean drifts. Specifically, we consider the critical (Lamperti-type) situation in which the mean drift at $x$ is about $c/x$. Our focus is the…

In this paper, we study the martingale property for a Scott correlated stochastic volatility model, when the correlation coefficient between the Brownian motion driving the volatility and the one driving the asset price process is…

Using results from our companion article [arXiv:1112.4824v2] on a Schauder approach to existence of solutions to a degenerate-parabolic partial differential equation, we solve three intertwined problems, motivated by probability theory and…

We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state…

Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal…

The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically…

Our goal in this paper is to study the market impact in a market in which the order flow is autocorrelated. We build a model which explains qualitatively and quantitatively the empirical facts observed so far concerning market impact. We…

As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…

A well known result in stochastic analysis reads as follows: for an $\mathbb{R}$-valued super-martingale $X = (X_t)_{0\leq t \leq T}$ such that the terminal value $X_T$ is non-negative, we have that the entire process $X$ is non-negative.…

We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…